Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T03:17:54.408Z Has data issue: false hasContentIssue false
  • English
  • Français

Formation of rhythmic sorted bed forms on the continental shelf: an idealised model

Published online by Cambridge University Press:  08 September 2011

Tomas Van Oyen ,
Huib de Swart  and
Paolo Blondeaux
Tomas Van Oyen*
Affiliation:
Department of Civil, Environmental and Architectural Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
Huib de Swart
Affiliation:
Institute for Marine and Atmospheric research Utrecht, Utrecht University, IMAU, PO Box 80005, NL-3508 TA Utrecht, The Netherlands
Paolo Blondeaux
Affiliation:
Department of Civil, Environmental and Architectural Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
*
†Email address for correspondence: tomas.vanoyen@ugent.be
Get access Rights & Permissions [Opens in a new window]

Abstract

An idealised model is presented to study the formation of sorted bed forms generated by a wind-driven along-shore current. The study employs a linear stability analysis to describe the time development of perturbations of both bottom composition and bed elevation, superimposed on a flat bed composed of a sediment mixture homogeneously distributed in space. The model considers both bed and suspended loads and takes into account the averaged influence of waves on the flow field and the transport of sediment. The results show that the positive coupling between waves, along-shore current and the erodible heterogeneous bed leads to the amplification of two modes, which exhibit distinct characteristics. A first mode is found to be dominant when moderate hydrodynamic conditions are considered and is primarily amplified by the convergence of sediment transport induced by the changes in the bed elevation. This mode has wavelengths of the order of hundred metres and has coarse (fine) sediments in its troughs (crests). By increasing the height of the waves and/or the strength of the steady current, the second mode can become dominant. This mode is characterised by shorter wavelengths and results from the interaction between the convergence of sediment transport related to changes in the bottom composition and that induced by perturbations of the bed elevation. These bed features can have an up-current or a down-current shift between the centre of the coarse-grained bands and the trough of the bottom wave. Typical growth times of the amplified features are of the order of hundreds of days and the migration rates, in the direction of the along-shore current, range between 0.1 and 10 m per day. A qualitative comparison of the model results with field observations indicates that the generation of two distinct modes provides a possible explanation for the broad range of characteristics of the natural bed features.

JFM classification

Geophysical and Geological Flows: Sediment transport
Type
Papers
Information
Journal of Fluid Mechanics , Volume 684 , 10 October 2011 , pp. 475 - 508
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Ashida, K. & Michiue, M. 1972 Study on hydraulic resistance and bedload transport rate in alluvial streams. Trans. Japan Soc. Civil Engrs 206, 59–69.Google Scholar
2. Aubrey, D. G., Twichell, D. C. & Pfirman, S. L. 1982 Holocene sedimentation in the shallow nearshore zone off Nauset inlet, Cape Cod, Massachusetts. Mar. Geol. 47, 243–259.CrossRefGoogle Scholar
3. Bellec, V. K., Bœ, R., Rise, L., Slagstad, D., Longva, O. & Dolan, M. F. J. 2010 Rippled scour depressions on continental shelf bank slopes off Nordland and Troms, northern Norway. Cont. Shelf Res. 1056–1069.CrossRefGoogle Scholar
4. Brownlie, W. R. 1981 Prediction of flow depth and sediment discharge in open channels. Tech Rep. W.M. Keck Lab. of Hydraulics and Water Resources, California Institute of Technology, Pasadena, California.Google Scholar
5. Cacchione, D. A., Grant, W. D. & Tate, G. B. 1984 Rippled scour depressions on the inner continental shelf off central California. J. Sedim. Petrol. 54, 1280–1291.Google Scholar
6. Christoffersen, J. V. & Jonsson, I. G. 1985 Bed friction and dissipation in a combined current and wave motion. Ocean Engng 12, 387–423.CrossRefGoogle Scholar
7. Coco, G., Murray, A. B. & Green, M. O. 2007a Sorted bed forms as self-organized patterns. Part 1. Model development. J. Geophys. Res. 112, F03015.Google Scholar
8. Coco, G., Murray, A. B., Green, M. O., Thieler, E. R. & Hume, T. M. 2007b Sorted bed forms as self-organized patterns. Part 2. Complex forcing scenarios. J. Geophys. Res. 112, F03016.Google Scholar
9. Colombini, M. 2004 Revisiting the linear theory of sand dune formation. J. Fluid Mech. 502, 1–16.CrossRefGoogle Scholar
10. Colombini, M. & Parker, G. 1995 Longitudinal streaks. J. Fluid Mech. 304, 161–183.CrossRefGoogle Scholar
11. Colombini, M. & Stocchino, A. 2005 Wind effect in turbulence parametrization. Adv. Water Resour. 28, 939–949.CrossRefGoogle Scholar
12. Dean, R. D. 1974 Aero report 74-11. Tech Rep. Imperial College, London.Google Scholar
13. Diesing, M., Kubicki, A., Winter, C. & Schwarzer, K. 2006 Decadal scale stability of sorted bedforms, German Bight, southeastern North Sea. Cont. Shelf. Res. 26, 902–916.CrossRefGoogle Scholar
14. Dodd, N. P., Blondeaux, P., Calvete, D., Falqués, A., de Swart, H. E., Hulscher, S. J. M. H., Rozynski, G. & Vittori, G. 2003 Understanding coastal morphodynamics using stability methods. J. Coast. Res. 19, 849–865.Google Scholar
15. Ferrini, V. L. & Flood, R. D. 2005 A comparison of rippled scour depressions identified with multibeam sonar: evidence of sediment transport in inner shelf environments. Cont. Shelf. Res. 25, 1979–1995.CrossRefGoogle Scholar
16. Fredsøe, J. & Deigaard, R. 1992 Mechanics of Coastal Sediment Transport, Advanced Series on Ocean Engineering , vol. 3. World Scientific.CrossRefGoogle Scholar
17. Goff, J. A., Mayer, L. A., Traykovski, P., Buynevich, I., Wilkens, R., Raymond, R., Glang, G., Evans, R. L., Olson, H. & Jenkins, C. 2005 Detailed investigation of sorted bedforms, or ‘rippled scour depressions,’ within the Martha’s Vineyard coastal observatory, Massachusetts. Cont. Shelf. Res. 25, 461–484.CrossRefGoogle Scholar
18. Gutierrez, B. T., Voulgaris, G. & Thieler, E. R. 2005 Exploring the persistence of sorted bedforms on the inner-shelf of Wrightsville beach, North Carolina. Cont. Shelf. Res. 25, 65–90.CrossRefGoogle Scholar
19. Hirano, M. 1971 On river bed degradation with armouring. Trans. Japan Soc. Civil Engrs 3 (2), 194–195.Google Scholar
20. Kleinhans, M. G. & van Rijn, L. C. 2002 Stochastic prediction of sediment transport in sand-gravel bed rivers. J. Hydraul. Engng 128, 412–425.CrossRefGoogle Scholar
21. Kovacs, A. & Parker, G. 1994 A new vectorial bedload formulation and its application to the time evolution of straight river channels. J. Fluid Mech. 267, 153–183.CrossRefGoogle Scholar
22. Lanzoni, S. & Tubino, M. 1999 Grain sorting and bar instability. J. Fluid Mech. 393, 149–174.CrossRefGoogle Scholar
23. Murray, A. B., Coco, G., Green, M. O., Hume, T. & Thieler, E. R. 2005 Different approaches to modeling inner shelf sorted bedforms. In 4th IAHR Symposium on River, Coastal and Estuarine Morphodynamics (ed. G. Parker & M. Garcia), pp. 1009–1015.Google Scholar
24. Murray, A. B. & Thieler, E. R. 2004 A new hypothesis and exploratory model for the formation of large-scale inner-shelf sediment sorting and ‘rippled scour depressions’. Cont. Shelf. Res. 24, 295–315.CrossRefGoogle Scholar
25. Parker, G. 1978 Self-formed straight rivers with equilibrium banks and mobile bed. Part 1. The sand-silt river. J. Fluid Mech. 89, 109–125.CrossRefGoogle Scholar
26. van Rijn, L. C. 1984 Sediment transport. Part 2. Suspended load transport. J. Hydraul. Engng 110, 1613–1641.CrossRefGoogle Scholar
27. van Rijn, L. C. 1991 Sediment transport in combined currents and waves. In Sand Transport in Rivers, Estuaries and the Sea (ed. Soulsby & Bettess). Euromech 262.Google Scholar
28. van Rijn, L. C. 1993 Principles of Sediment Transport in Rivers, Estuaries and Coastal Seas. Aqua.Google Scholar
29. Schwab, W. C., Thieler, E. R., Allen, J. R., Foster, D. S., Swift, B. A. & Denny, J. F. 2000 Influence of inner-continental shelf geologic framework on the evolution and behavior of the barrier-island system between Fire Island Inlet and Shinnecock Inlet, Long Island, New York. J. Coast. Res. 16, 408–422.Google Scholar
30. Seminara, G., Colombini, M. & Parker, G. 1996 Nearly pure sorting waves and formation of bedload sheets. J. Fluid Mech. 312, 253–278.CrossRefGoogle Scholar
31. Soulsby, R. L. 1997 Dynamics of Marine Sands. Thomas Telford.Google Scholar
32. Soulsby, R. L. & Whitehouse, J. S. 2005 Prediction of ripple properties in shelf seas. Tech Rep. 150. Wallingford Ltd.Google Scholar
33. de Swart, H. E., Walgreen, M., Calvete, D. & Vis-Star, N. C. 2008 Nonlinear modelling of shoreface-connected ridges: impact of grain sorting and interventions. Coast. Engng 55, 642–656.CrossRefGoogle Scholar
34. Thieler, E. R., Plikey, O. H., Cleary, W. J. & Schwab, W. C. 2001 Modern sedimentation on the shoreface and inner continental shelf at Wrightsville beach, North Carolina, USA. J. Sedim. Res. 71, 958–970.CrossRefGoogle Scholar
35. Thieler, E. R., Schwab, W. C. & Cacchione, D. A. 1998 Wave and current measurements in a cross-shore scour depression on the shoreface off Wrightsville beach, North Carolina. Eos Trans. AGU 79 (1) supplement, OS61.Google Scholar
36. Van Dorn, W. C. 1953 Wind stress on an artificial pond. J. Mar. Res. 12, 249–276.Google Scholar
37. Van Oyen, T. 2010 Sediment sorting in coastal seas. PhD thesis, University of Genoa.Google Scholar
38. Van Oyen, T. & Blondeaux, P. 2009 Grain sorting effects on the formation of tidal sand waves. J. Fluid Mech. 629, 311–342.CrossRefGoogle Scholar
39. Van Oyen, T., de Swart, H. E. & Blondeaux, P. 2010 Bottom topography and roughness variations as triggering mechanisms to the formation of sorted bedforms. Geophys. Res. Lett. 37, L18401.CrossRefGoogle Scholar
40. Vis-Star, N. C., de Swart, H. E. & Calvete, D. 2009 Effect of wave–bedform feedbacks on the formation of, and grain sorting over shoreface-connected sand ridges. Ocean Dyn 59, 731–749.CrossRefGoogle Scholar
41. Walgreen, M., de Swart, H. E. & Calvete, D. 2003 Effect of grain size sorting on the formation of shoreface-connected sand ridges. J. Geophys. Res. 108, C3.CrossRefGoogle Scholar